How to make fire flow from one point of an object to another
Quickest way I could work out:
Use a 'screw' modifier on a circle, with an animated angle (and an empty to rotate the circle around), then use this as the emitter. You'd probably want to put it inside your torus object and make it not render.
This works in Blender 2.81a (old smoke sim) and Mantaflow (November 26th 2019 build).
here's what it looks like- https://youtu.be/7h7JBEYuu1Q

And here's the .blend file (old 2.81a smoke sim) to pull apart- https://www.dropbox.com/s/zfctf8g5x31j9iu/FireReveal01.blend?dl=0

I tried using a simple wipe white-over-black image sequence as a UV mapped texture on the emitter/flow object, but both the old smoke sim and Mantaflow ignored it (just got a quarter of the torus on fire that didn't move) so don't waste your time with that!